Harnessing Unimodality in Semiparametric Contextual Pricing via Oracle Price Map Learning

arXiv:2605.15411v1 Announce Type: cross Abstract: We study contextual dynamic pricing in a semiparametric scalar-index valuation model where the latent value is v_t=mu_ast(mathsf c_t)+xi_t, with an unknown utility map mu_ast and an unknown additive noise distribution. The key decision object is the one-dimensional oracle price map umapsto p^ast(u) induced by the scalar index u=mu_ast(mathsf c) and the noise tail. Under the eta-Holder smoothness of the tail function for etageq 2 and a revenue-geometry condition that gives a unique, stable, interior maximizer, this oracle map is itself (eta-1)-smooth. We exploit such structure through mathsf{ORBIT}, a modular coarse-to-fine policy that takes a scalar pilot index as input, localizes a benchmark price in each active bin, and learns a local polynomial approximation of the oracle map inside a trust region via bandit convex optimization. For the baseline linear utility model mu_ast(mathsf c)=mathsf c^opheta_ast, an adaptive elliptical exploration scheme constructs the required scalar pilot online without distributional assumptions on the contexts. The resulting policy achieves regret widetilde{O}ig(T^{frac{2eta-1}{4eta-3}}+sqrt{dT}ig). For fixed d, we establish a matching lower bound in the horizon dependence, unveiling that the nonparametric oracle-map learning term is minimax sharp. The same scalar-pilot interface also yields extensions to sparse high-dimensional linear utility and nonparametric Holder utility.

Source: arXiv cs.LG | 2026-05-18